A New Solution for The Enzymatic Glucose Fuel Cell Model with Morrison Equation via Haar Wavelet Collocation Method

摘要

Integral equations are essential tools in various areas of applied mathematics. A computational approach to solving an integral equation is important in scientific research. The Haar wavelet collocation method (HWCM) with operational matrices of integration is one famous method which has been applied to solve systems of linear integral equations. In this paper, an approximated analytical method based on the Haar wavelet collocation method is applied to the system of diffusion convection partial differential equations with initial and boundary conditions. This system determines the enzymatic glucose fuel cell with the chemical reaction rate of the Morrison equation. The enzymatic glucose fuel cell model describes the concentration of glucose and hydrogen ion that can be converted into energy. During the process, the model reduces to the linear integral equation system including computational Haar matrices. The computational Haar matrices can be computed by HWCM coding in the Maple program. Illustrated examples are provided to demonstrate the preciseness and effectiveness of the proposed method. The results are shown as numerical solutions of glucose and hydrogen ion.